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Scaling and allometry in the building geometries of Greater London

Author

Listed:
  • M. Batty
  • R. Carvalho
  • A. Hudson-Smith
  • R. Milton
  • D. Smith
  • P. Steadman

Abstract

Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal structure. We redress this here by examining scaling relationships in a world city using data on the geometric properties of individual buildings. We first summarise how power laws can be used to approximate the size distributions of buildings, in analogy to city-size distributions which have been widely studied as rank-size and lognormal distributions following Zipf [Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge, 1949)] and Gibrat [Les Inégalités Économiques (Librarie du Recueil Sirey, Paris, 1931)]. We then extend this analysis to allometric relationships between buildings in terms of their different geometric size properties. We present some preliminary analysis of building heights from the Emporis database which suggests very strong scaling in world cities. The data base for Greater London is then introduced from which we extract 3.6 million buildings whose scaling properties we explore. We examine key allometric relationships between these different properties illustrating how building shape changes according to size, and we extend this analysis to the classification of buildings according to land use types. We conclude with an analysis of two-point correlation functions of building geometries which supports our non-spatial analysis of scaling. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Suggested Citation

  • M. Batty & R. Carvalho & A. Hudson-Smith & R. Milton & D. Smith & P. Steadman, 2008. "Scaling and allometry in the building geometries of Greater London," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 303-314, June.
  • Handle: RePEc:spr:eurphb:v:63:y:2008:i:3:p:303-314
    DOI: 10.1140/epjb/e2008-00251-5
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    Citations

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    Cited by:

    1. Chen, Yanguang, 2014. "An allometric scaling relation based on logistic growth of cities," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 65-77.
    2. Thill, Jean-Claude & Dao, Thi Hong Diep & Zhou, Yuhong, 2011. "Traveling in the three-dimensional city: applications in route planning, accessibility assessment, location analysis and beyond," Journal of Transport Geography, Elsevier, vol. 19(3), pages 405-421.
    3. Alaa Krayem & Aram Yeretzian & Ghaleb Faour & Sara Najem, 2021. "Machine learning for buildings’ characterization and power-law recovery of urban metrics," PLOS ONE, Public Library of Science, vol. 16(1), pages 1-13, January.
    4. Daniel Czamanski & Rafael Roth, 2011. "Characteristic time, developers’ behavior and leapfrogging dynamics of high-rise buildings," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 46(1), pages 101-118, February.
    5. Hiroyuki Usui, 2024. "Relative spatial variability in building heights and its spatial association: Application for the spatial clustering of harmonious and inharmonious building heights in Tokyo," Environment and Planning B, , vol. 51(4), pages 987-1002, May.
    6. Haosu Zhao & Bart Julien Dewancker & Feng Hua & Junping He & Weijun Gao, 2020. "Restrictions of Historical Tissues on Urban Growth, Self-Sustaining Agglomeration in Walled Cities of Chinese Origin," Sustainability, MDPI, vol. 12(14), pages 1-29, July.
    7. Stepinski, Tomasz F. & Dmowska, Anna, 2020. "Complexity in patterns of racial segregation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Fatemeh Jahanmiri & Dawn Cassandra Parker, 2022. "An Overview of Fractal Geometry Applied to Urban Planning," Land, MDPI, vol. 11(4), pages 1-23, March.
    9. Chen, Yanguang, 2017. "Multi-scaling allometric analysis for urban and regional development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 673-689.
    10. Paul J. Maliszewski & Breandán Ó hUallacháin, 2012. "Hierarchy and concentration in the American urban system of technological advance," Papers in Regional Science, Wiley Blackwell, vol. 91(4), pages 743-758, November.
    11. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    12. Pedro Plasencia-Lozano, 2018. "An approach to determine the frequency of bridges in an urban context: The case of European cities," Environment and Planning B, , vol. 45(4), pages 649-668, July.
    13. Alan Penn & Kinda Al Sayed, 2017. "Spatial information models as the backbone of smart infrastructure," Environment and Planning B, , vol. 44(2), pages 197-203, March.
    14. Krzysztof Cebrat & Maciej Sobczyński, 2016. "Scaling Laws in City Growth: Setting Limitations with Self-Organizing Maps," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-11, December.
    15. Chen, Yanguang & Wang, Yihan & Li, Xijing, 2019. "Fractal dimensions derived from spatial allometric scaling of urban form," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 122-134.
    16. Pierpaolo Andriani & Bill McKelvey, 2009. "Perspective ---From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations," Organization Science, INFORMS, vol. 20(6), pages 1053-1071, December.
    17. Chunyan Wang & Hanying Jiang & Hao Wu & Yi Liu & Siyue Guo & Ming Xu, 2023. "Scaling in urban building energy use and its influencing factors," Journal of Industrial Ecology, Yale University, vol. 27(4), pages 1076-1088, August.

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